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1. Field of the Invention
The present invention generally relates to seismic data processing. More specifically, the invention relates to computing coherency values corresponding to edges of seismic reflections to assist in locating subsurface faults, channels and other geological entities using eigenvalue, maximum entropy, or maximum likelihood analysis.
2. Background of the Invention
The field of seismology focuses on the use of artificially generated elastic waves to locate mineral deposits such as hydrocarbons, ores, water, and geothermal reservoirs. Seismology also is used for archaeological purposes and to obtain geological information for engineering. Exploration seismology provides data that, when used in conjunction with other available geophysical, borehole, and geological data, can provide information about the structure and distribution of rock types and contents.
Most oil companies rely on seismic interpretation to select sites for drilling exploratory oil wells. Despite the fact that the seismic data is used to map geological structures rather than find petroleum directly, the gathering of seismic data has become a vital part of selecting the site of exploratory and development wells. Experience has shown that the use of seismic data greatly improves the likelihood of a successful venture.
Seismic exploration generally involves a multitude of equipment placed on the ground. At least one piece of equipment creates and imparts vibrational energy into the ground. That energy may be in the form of a relatively short duration, large amplitude xe2x80x9cimpulsexe2x80x9d or longer duration, lower amplitude vibrations. The energy imparted to the ground propagates generally downward and reflects off various subsurface structures, such as interfaces between different rock formations. The reflected energy waves propagate back upward to the surface and are detected by sensors called xe2x80x9cgeophones.xe2x80x9d
In seismic exploration it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone spatial location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the recorded data can be processed by a computer in known ways to produce an image of the subsurface. The image thus produced is commonly interpreted by geophysicists to detect the presence of hydrocarbons.
A xe2x80x9cseismogramxe2x80x9d is the record recorded from a geophone. Seismograms are commonly recorded as digital samples representing the amplitude of a received seismic signal as a function of time. Because seismograms are usually obtained along several lines of exploration on the surface of the earth, the digital samples can be formed into a 3-dimensional array with each sample in the array representing the amplitude of the seismic signal as a function of time (t) and position on the earth (x,y). The collection of seismic samples as a function of time (t) for one position in the earth is referred to as a xe2x80x9cseismic trace.xe2x80x9d The collection of seismic traces forming an array are commonly referred to as xe2x80x9cseismic data volumes.xe2x80x9d
A seismic data volume depicts the subsurface layering of a portion of the earth. It is the principal tool that a geophysicist uses to determine the nature of the earth""s subsurface formations. The seismic data volume can be studied either by plotting it on paper or displaying it on a computer monitor. A geophysicist then can interpret the information. When displaying the seismic data volume along a principle direction, crosslines, inlines, time slices, or horizon slices can be made. The seismic data volume can be mathematically processed in accordance with known techniques to make subtle features in the seismic data more discernable. The results of these processing techniques are known as seismic xe2x80x9cattributes.xe2x80x9d
Several types of seismic attributes are useful, such as those disclosed in xe2x80x9cComplex Seismic Trace Analysisxe2x80x9d by Tanner, Koehler, and Sheriff, 1979, Geophysics, vol. 44, no. 6, pp. 1041-1063, incorporated herein by reference in its entirety. The instantaneous phase attribute, for example, is generally insensitive to amplitude and measures the continuity of seismic events. It can be used to show subtle unconformities where subsurface layers are truncated by an erosion surface. Further, the apparent polarity attribute has been used to discern between gas and water containing reservoirs. The reflection strength attribute has been used to discern between chalk (high amplitude) and sands/shales (low amplitude). Such attributes are known as complex trace attributes and are derived by using the well-known Hilbert Transform.
These complex trace attributes operate on individual seismic traces. Neidel and Taner, 1971, Geophysics, vol. 36, no. 6, p. 482-497 introduced the concept of semblance or coherency which measures the trace-to-trace continuity of seismic events. Neidel and Taner measured the coherency to determine the velocity of seismic events. Coherency can also be used to determine the edges of seismic events to enable the interpretation of subtle faults and channels in the subsurface when displayed along time slices or horizon slices. Coherency measures the similarity between adjacent seismic samples. When the seismic samples are similar to one another, such as would be the case for reflections along a continuous subsurface formation, the coherency will generally be high. Conversely, when the seismic samples are dissimilar, such as across a fault cutting a subsurface formation, the coherency will be much lower. By measuring the degree of coherency in the seismic data volume, subsurface faults and other features that disturb the continuity of seismic events can be detected and interpreted by geophysicists.
Various techniques for determining coherency have been suggested. For example, in U.S. Pat. No. 5,563,949 to Bahorich and Farmer, the seismic data volume is divided into horizon slices in which the data is separated along reflections. These horizon slices are then divided into cells that contain seismic data along the inline and crossline directions. The xe2x80x9csimilarityxe2x80x9d is measured for both the inline and crossline traces, and the result combined into a coherency estimate for that particular cell. Bahorich and Fanner""s algorithm continues until estimates of coherency are determined for all cells within the seismic data volume. In Bahorich""s method the similarity is measured by searching for the maximum cross-correlation value in the neighboring traces. In some cases because of noise or other types of interference this search disadvantageously may not represent the overall similarity of the actual seismic data. Furthermore, Bahorich""s method only uses traces in the inline and crossline direction, but not in other directions.
In U.S. Pat. No. 5,940,778 to Marfurt, Kirlin, and Gersztenkorn the seismic data volume is divided into cells containing at least three traces inline, three traces in the crossline direction, and five seismic samples in time. These seismic samples are formed into a data matrix. A xe2x80x9csimilarityxe2x80x9d matrix is then calculated from this data matrix. Then, the principle xe2x80x9ceigenvaluexe2x80x9d (a mathematical quantity well-known to those of ordinary skill in the art) is calculated from the similarity matrix. A measure of the power in the similarity matrix is then calculated by computing the matrix trace of the similarity matrix. The coherency is finally calculated by dividing the principle eigenvalue by the trace of the similarity matrix. Marfurt et al""s algorithm continues until estimates of coherency are determined for all cells within the seismic data volume. Marfurt and Gertztenkorn""s methods calculate the eigenvalues from a similarity matrix calculated from the seismic data and, as such, is relatively complex, computationally intensive and inaccurate for smaller eigenvalues. Furthermore, Marfurt et al method uses the seismic data without any enhancement to remove noise and other artifacts.
The methods of Bahorich et al and Marfurt et al provide generally satisfactory techniques for determining coherency of a seismic data volume to determine the positions of subsurface faults, channels and other subtle geological features that cause discontinuities in the seismic data volume. These techniques, however, are not without various disadvantages such as those noted above. Accordingly, a technique for determining coherency of a seismic data volume that addresses these issues is needed.
The problems noted above are solved in large part by a seismic data processing system and method. The system processes seismic data that has been acquired in the field and pre-processed in a suitable manner. Then, a subset of the seismic data volume or the entire cube is chosen for analysis. This subset might be between known reservoirs, along a geologic horizon of interest, shallow areas to determine geologic hazards before drilling, or other area of interest. Beginning at a selected spatial and temporal position in the subset seismic data volume, a subset seismic sample volume is selected surrounding this position containing several seismic samples defined by a rectangular box. These seismic samples are then placed in an m by n data matrix, where m represents the number of seismic spatial positions x,y, and n represents the number of seismic time samples. This m by n data matrix is then subject to singular value decomposition to compute n eigenvalues. The coherence of this particular data is then calculated by raising the maximum eigenvalue to a power k selected by the user and dividing this value by the sum of all the eigenvalues raised to the same value k. This coherence value is then saved to another coherence seismic data volume. The algorithm repeats at the next temporal position and then in the spatial x and y positions until coherency estimates are computed for all positions in the selected subset of the seismic data volume of interest. The coherency estimates can then be analyzed for useful information regarding the existence and location of various types of geologic formations, such as faults.
In an alternate embodiment, the cosine of the instantaneous phase attribute of the seismic sample is calculated using several seismic samples around the sample. The calculated cosine of the phase is stored into the m by n data matrix instead of the seismic data itself. This removes amplitude information from the seismic data trace, reducing noise and making the coherence estimate more effective. The algorithm then proceeds as described above.
In an alternative embodiment to computing eigenvalues, the coherency estimate is computed either using a maximum likelihood technique or a maximum entropy technique. Both of these latter techniques involve computing a covariance matrix, normalizing the covariance matrix and computing the coherency estimate as a function of the inverse of the covariance matrix.
Accordingly, the subject matter described herein provides an effective technique of calculating a coherency estimate for a volume of seismic data so that subtle geologic features such as faults and channels can be more easily seen by geophysicists. These and other advantages will become apparent upon reviewing the following disclosure.